These results, which are known to be exact to second-order in the heterogeneity contrast, are found to satisfy all known bounds.
The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated.
Solids 44 (1996) 827) makes use of the "tangent" moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases.
Solids 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast.
When a focal male approached the antenna (<10 cm), arrivals and departures were registered and saved <span class="lh">exact to the second.
It can be argued that the size of these correction terms is proportional to the bimolecular reaction rate constants since the LNA is exact up to second moments for networks composed solely of unimolecular reactions since the propensities are linear functions of the concentrations (see section Methods).
More specifically, the dynamic optimization problem is solved using (i) direct collocation on finite elements to obtain a finite dimensional optimization problem, and (ii) automatic differentiation to calculate exact first and second order information.
Here, we extensively study the performance of the NEKF which uses the exact first and second order nonlinear statistics without any approximations due to linearization.
The true locations and the locations of the peaks after matched filtering are exact up to the second decimal place w.r.t the range.
The eigenvalue problem governing the harmonic propagation in the micropolar non-centrosymmetric continuum results in general characterized by a hermitian full matrix that is exact up to the second order in the wave vector.
Following descriptive statistics, Pearson chi-square tests and Fisher's exact tests were used to first examine the association between location of care and decedent and informant characteristics and informant perceptions of the domains of care.
